Distribution moments

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Distribution moments

Moments are measures that tell us something about a distribution (e.g., does it have fat tails?). The first four moments are the following. Mean: a measure of central tendency (a.k.a., location). Variance: a measure of dispersion or scatter (a.k.a., scale). Skew: a measure of symmetry or asymmetry (Normal skew = 0). Kurtosis: a measure of peakedness and tail-heaviness (a.k.a., shape) A normal has kurtosis = 3 and so "excess kurtosis" of 0. At the end of the tutorial, I test the skew and kurtosis of Yahoo's (YHOO) daily returns over the past ten years, using Excel's built-in functions =SKEW() and = KURT(). The results are typical for equity returns: positive skew and excess kurtosis (fat tails).

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